Problem: Solve for $x$ and $y$ using elimination. ${x-3y = 6}$ ${-x+5y = -4}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $2y = 2$ $\dfrac{2y}{{2}} = \dfrac{2}{{2}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x-3y = 6}\thinspace$ to find $x$ ${x - 3}{(1)}{= 6}$ $x-3 = 6$ $x-3{+3} = 6{+3}$ ${x = 9}$ You can also plug ${y = 1}$ into $\thinspace {-x+5y = -4}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(1)}{= -4}$ ${x = 9}$